Skip to main content
Log in

Capture Performance of A Multi-Freedom Wave Energy Converter with Different Power Take-off Systems

China Ocean Engineering Aims and scope Submit manuscript


Among the wave energy converters (WECs), oscillating buoy is a promising type for wave energy development in offshore area. Conventional single-freedom oscillating buoy WECs with linear power take-off (PTO) system are less efficient under off-resonance conditions and have a narrow power capture bandwidth. Thus, a multi-freedom WEC with a nonlinear PTO system is proposed. This study examines a multi-freedom WEC with 3 degrees of freedom: surge, heave and pitch. Three different PTO systems (velocity-square, snap through, and constant PTO systems) and a traditional linear PTO system are applied to the WEC. A time-domain model is established using linear potential theory and Cummins equation. The kinematic equation is numerically calculated with the fourth-order Runge-Kutta method. The optimal average output power of the PTO systems in all degrees of freedom are obtained and compared. Other parameters of snap through PTO are also discussed in detail. Results show that according to the power capture performance, the order of the PTO systems from the best to worst is snap through PTO, constant PTO, linear PTO and velocity-square PTO. The resonant frequency of the WEC can be adjusted to the incident wave frequency by choosing specific parameters of the snap through PTO. Adding more DOFs can make the WEC get a better power performance in more wave frequencies. Both the above two methods can raise the WEC’s power capture performance significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions


  • Albatern Wave Energy, 2017. How WaveNET Works, [2017-01-06].

  • Babarit, A., 2015. A database of capture width ratio of wave energy converters, Renewable Energy, 80, 610–628.

    Article  Google Scholar 

  • Babarit, A., Hals, J., Muliawan, M.J., Kurniawan, A., Moan, T. and Krokstad, J., 2012. Numerical benchmarking study of a selection of wave energy converters, Renewable Energy, 41, 44–63.

    Article  Google Scholar 

  • Bai, O., Yokouchi, H., Gunawardane, S.D.G.S.P. and Thakker, A., 2002. Heave and pitch buoy (HPB), a miniature wave energy converter, Proceedings of the 12th International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, Kitakyushu, Japan, pp. 649–654.

    Google Scholar 

  • Bhatt, J., Carthy, J., Clark, T., Galea, S., Sutch, A., Tutt, A. and Walker, J., 2016. Optimisation and Development of A Multi-Axis Wave Energy Converter Device, Master of Engineering Project Report, Engineering Department, Lancaster University.

    Google Scholar 

  • Bozzi, S., Miquel, A.M., Antonini, A., Passoni, G. and Archetti, R., 2013. Modeling of a point absorber for energy conversion in Italian Seas, Energies, 6(6), 3033–3051.

    Article  Google Scholar 

  • Budar, K. and Falnes, J., 1975. A resonant point absorber of oceanwave power, Nature, 256(5517), 478–479.

    Article  Google Scholar 

  • Cummins, W.E., 1962. The Impulse Response Function and Ship Motions, David Taylor Model Basin, Washington DC, pp. 56–60.

    Google Scholar 

  • de Koker, K.L., Crevecoeur, G., Meersman, B., Vantorre, M. and Vandevelde, L., 2017. A wave emulator for ocean wave energy. a Froude-scaled dry power take-off test setup, Renewable Energy, 105, 712–721.

    Article  Google Scholar 

  • de O. Falcão, A.F., 2007. Modelling and control of oscillating-body wave energy converters with hydraulic power take-off and gas accumulator, Ocean Engineering, 34(14–15), 2021–2032.

    Article  Google Scholar 

  • de O. Falcão, A.F., 2008. Phase control through load control of oscillating-body wave energy converters with hydraulic PTO system, Ocean Engineering, 35(3–4), 358–366.

    Article  Google Scholar 

  • Evans, D.V., 1976. A theory for wave-power absorption by oscillating bodies, Journal of Fluid Mechanics, 77(1), 1–25.

    Article  MATH  Google Scholar 

  • Heikkinen, H., Lampinen, M.J. and Böling, J., 2013. Analytical study of the interaction between waves and cylindrical wave energy converters oscillating in two modes, Renewable Energy, 50, 150–160.

    Article  Google Scholar 

  • Iijima, T., Taya, T., Watabe, T., Kondo, H., Yokouchi, H. and Gunawarudane, S.P., 2000. Characteristics of heave & pitch buoy type wave energy converter system, Proceedings of Civil Engineering in the Ocean, 16, 239–244.

    Article  Google Scholar 

  • Kim, S.J., Shin, M.J. and Koo, W., 2016. A numerical study on a floating hemisphere wave energy converter with hydraulic PTO system, Proceedings of the OCEANS 2016 — Shanghai, IEEE, Shanghai, China, pp. 1–5.

    Google Scholar 

  • Li, Y.C. and Teng, B., 2002. Wave Action on Maritime Structures, Second ed., China Ocean Press, Beijing. (in Chinese)

    Google Scholar 

  • McCabe, A.P., Aggidis, G.A. and Widden, M.B., 2010. Optimizing the shape of a surge-and-pitch wave energy collector using a genetic algorithm, Renewable Energy, 35(12), 2767–2775.

    Article  Google Scholar 

  • Mei, C.C., 2012. Hydrodynamic principles of wave power extraction, Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 370(1959), 208–234.

    Article  MathSciNet  MATH  Google Scholar 

  • Newman, J.N., 1976. The interaction of stationary vessels with regular waves, Proceedings of the 11th Symposium on Naval Hydrodynamics, Mechanical Engineering Publications Limited, London, pp. 491–501.

    Google Scholar 

  • Ogilvie, T.F., 1964. Recent Progress towards the understanding and prediction of ship motions, Proceedings of the 5th Symposium on Naval Hydrodynamics, Maritime and Transport Technology, Bergen, Norway.

    Google Scholar 

  • Osborne, J., Rawcliffe, P., Tarrant, H., Wheatland, W., Lovett, M., Tailyour, J., Veryard, P., Woodall, A. and Jesson, P., 2015. Multiaxis Wave Energy Converter, Master of Engineering Project Report, Engineering Department, Lancaster University.

    Google Scholar 

  • Shan, P.H., 2013. Time-Domain Coupling Analysis of Deepwater Floating Platform and the Mooring Lines, MSc. Thesis, Harbin Engineering University, Harbin. (in Chinese)

    Google Scholar 

  • Shi, H.D., Cao, F.F., Liu, Z. and Qu, N., 2016. Theoretical study on the power take-off estimation of heaving buoy wave energy converter, Renewable Energy, 86, 441–448.

    Article  Google Scholar 

  • Sjökvist, L., Wu, J.M., Ransley, E., Engström, J., Eriksson, M. and Göteman, M., 2017. Numerical models for the motion and forces of point-absorbing wave energy converters in extreme waves, Ocean Engineering, 145, 1–14.

    Article  Google Scholar 

  • Wang, D., 2015. Optimization of Combined Oscillating Buoys’ Array Layout, MSc. Thesis, Ocean University of China. (in Chinese)

    Google Scholar 

  • Xiao, X.L., Xiao, L.F. and Peng, T., 2017. Comparative study on power capture performance of oscillating-body wave energy converters with three novel power take-off systems, Renewable Energy, 103, 94–105.

    Article  Google Scholar 

  • Ye, Y.Z. and Chen, W.D., 2017. Frequency- and time-domain analysis of a multi-degree-of-freedom point absorber wave energy converter, Advances in Mechanical Engineering, 9(12), 1–10.

    Google Scholar 

  • Zhang, D.H., George, A., Wang, Y.F., Gu, X.X., Li, W. and Chen, Y., 2015. Wave tank experiments on the power capture of a multi-axis wave energy converter, Journal of Marine Science and Technology, 20(3), 520–529.

    Article  Google Scholar 

  • Zhang, X.T. and Yang, J.M., 2015. Power capture performance of an oscillating-body WEC with nonlinear snap through PTO systems in irregular waves, Applied Ocean Research, 52, 261–273.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Hong-da Shi.

Additional information

Foundation item: This paper is financially supported by the Shandong Provincial Natural Science Key Basic Program (Grant No. ZR2017ZA0202), the Qingdao Municipal Science & Technology Program (Grant No. 15-8-3-7-jch) and Special Project for Marine Renewable Energy (Grant No. GHME2016YY02).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, St., Shi, Hd. & Dong, Xc. Capture Performance of A Multi-Freedom Wave Energy Converter with Different Power Take-off Systems. China Ocean Eng 33, 288–296 (2019).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words